On Fourier Series in the Context of Jacobi Matrices

被引：0

作者：

Matos, Jose M. A. ^{[1
]}

Vasconcelos, Paulo B. ^{[2
]}

Matos, Jose A. O. ^{[2
]}

机构：

[1] Univ Porto, Inst Super Engn, Inst Politecn Porto, Ctr Matemat, Rua Dr Antonio Bernardino de Almeida 431, P-4249015 Porto, Portugal

[2] Univ Porto, Fac Econ, Ctr Matemat, Rua Dr Roberto Frias S-N, P-4200464 Porto, Portugal

来源：

AXIOMS | 2024年 / 13卷 / 09期

关键词：

orthogonal polynomials; fourier series; Jacobi matrix; functions of matrices; spectral methods; CONNECTION COEFFICIENTS; LINEARIZATION FORMULAS; POLYNOMIALS;

D O I：

10.3390/axioms13090581

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the properties of matrices that emerge from the application of Fourier series to Jacobi matrices. Specifically, we focus on functions defined by the coefficients of a Fourier series expressed in orthogonal polynomials. In the operational formulation of integro-differential problems, these infinite matrices play a fundamental role. We have derived precise calculation formulas for their elements, enabling exact computation of these operational matrices. Numerical results illustrate the effectiveness of our approach.

引用

页数：16

共 50 条

[21] On Fourier series of Jacobi-Sobolev orthogonal polynomials
Marcellán, F
Osilenker, BP
Rocha, IA
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2002, 7 (05) : 673 - 699
[22] Determination of a Jump by Conjugate Fourier-Jacobi Series
Sadikovic, Samra
FILOMAT, 2018, 32 (08) : 2745 - 2754
[23] On a Method for Uniform Summation of the Fourier-Jacobi Series
Alexandra Diana Meleşteu
Radu Păltănea
Results in Mathematics, 2022, 77
[24] THE JACOBI POLYNOMIAL CONVERGENCE OF THE FOURIER-SERIES IN THE MEAN
KHODAK, LB
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1982, (08): : 28 - 30
[25] PERTURBATION SERIES FOR JACOBI MATRICES AND THE QUANTUM RABI MODEL
Charif, Mirna
Zielinski, Lech
OPUSCULA MATHEMATICA, 2021, 41 (03) : 301 - 333
[26] Applications of Hankel and Regular Matrices in Fourier Series
Alotaibi, Abdullah
Mursaleen, M.
ABSTRACT AND APPLIED ANALYSIS, 2013,
[27] On the convergence of random Fourier-Jacobi series of continuous functions
Maharana, Partiswari
Sahoo, Sabita
arXiv, 2022,
[28] QUASI FOURIER-JACOBI SERIES AND A KIND OF NEW APPROXIMATION
Zhang Peixuan (Shandong University
Approximation Theory and Its Applications, 1995, (01) : 80 - 93
[29] Fourier-Jacobi coefficients of Eisenstein series on unitary groups
Zhang, Bei
ALGEBRA & NUMBER THEORY, 2013, 7 (02) : 283 - 337
[30] On Fourier series of a discrete Jacobi-Sobolev inner product
Marcellán, F
Osilenker, BP
Rocha, IA
JOURNAL OF APPROXIMATION THEORY, 2002, 117 (01) : 1 - 22

← 1 2 3 4 5 →